Joe Willock scored the third goal towards half time to ensure the Gunners secure top place in their group with one match to go.
After all the chaos ahead of this Europa League encounter, it was calmness from Arsenal's unfazed youngsters that finally put an end to the Poltava palaver once and for all.
Unai Emery's side won to ensure they qualify top of Group E, with two teenagers in Emile Smith Rowe and Joe Willock scoring to extend their unbeaten run to 18 games.
It was –10C at kick-off and at one point, the referee had to replace his can of spray because it was frozen stiff. Nevertheless, Arsenal's team of starlets kept their cool in the icy conditions.
Arsenal will now head into their Premier League meeting with Tottenham Hotspur looking to make it 19 matches unbeaten. Emery knows it will be nowhere near as easy as this.
Elsewhere, Olivier Giroud scored a brace as Chelsea beat Paok Salonika four nil at Stamford Brige. Hudson Odoi and Alvaro Morata were on target too.
Callum Hudson-Odoi may only be 18 years old and the opponents, admittedly, were porous after being reduced to 10 men inside seven minutes, but this remained a performance to remember from a teenager who formed an integral part of England's Under 17 World Cup triumph last year.
The winger had previously been limited to only 35 minutes of Europa League action this season and has not appeared in the Premier League or Carabao Cup. His slow progress has frustrated fans and the pressure on Sarri to hand more opportunities to the player will only grow after this display.